Method and apparatus for measurement of a characteristic of an optical system

ABSTRACT

Disclosed embodiments may include a device, system and method for providing a low cost device that can measure refractive errors very accurately via attachment to a smart phone. A disclosed device may use ambient light or a light source in simulating the cross cylinder procedure that optometrists use by utilizing the inverse Shack-Hartman technique. The optical device may include an array of lenslets and pinholes that will force the user to effectively focus at different depths. Using an optical device, in conjunction with a smart phone, the user first changes the angle of the axis until he/she sees a cross pattern (the vertical and horizontal lines are equally spaced). The user adjusts the display, typically using the controls on the smartphone, to make the lines come together and overlap, which corresponds to bringing the view into sharp focus, thus determining the appropriate optical prescription for the user.

RELATED PATENT APPLICATION AND INCORPORATION BY REFERENCE

This is a Continuation in Part (CIP) utility application based upon andclaiming priority from U.S. patent application Ser. No. 16/276,302 filedon Feb. 14, 2019 which is a CIP of U.S. patent application Ser. No.15/491,557 filed on Apr. 19, 2017 and now U.S. Pat. No. 10,206,566issued on Feb. 19, 2019, which claims priority from provisional patentapplication Ser. No. 62/409,276 filed on Oct. 17, 2016. This applicationalso claims the benefit and priority of provisional patent application62/813,488 filed on Mar. 4, 2019.The related applications areincorporated herein by reference and made a part of this application. Ifany conflict arises between the disclosure of the invention in thisutility application and that in the related applications, the disclosurein this utility application shall govern. Moreover, the inventor(s)incorporate herein by reference any and all patents, patentapplications, and other documents hard copy or electronic, cited orreferred to in this application.

COPYRIGHT AND TRADEMARK NOTICE

This application includes material which is subject or may be subject tocopyright and/or trademark protection. The copyright and trademarkowner(s) has no objection to the facsimile reproduction by any of thepatent disclosure, as it appears in the Patent and Trademark Officefiles or records, but otherwise reserves all copyright and trademarkrights whatsoever.

BACKGROUND OF THE INVENTION (1) Field of the Invention

The invention generally relates to optometers and the assessment ofrefractive disorders of the human eye. More particularly, the inventionrelates to the use of hand held consumer devices used forself-refraction.

(2) Background

Disclosed embodiments may measure the refractive properties of anoptical system by simulating the cross-cylinder procedure thatoptometrists use in a clinical setting. An optical system as definedherein can include, but is not limited to, the human eye and mechanicalsystems wherein refractive measurement can determine a refractive error.Disclosed embodiments may comprise extensions and improvements upon themethods described in published patent application US 2013/0027668 A1 byPamplona et al which discloses the creation of a low cost device thatcan measure refractive errors using a smart phone as a light source.However, the method and device described in the prior art is limited tooptical systems consisting of a single multi-lens array or a pin holearray, which is neither as accurate and easy to use nor as economical asthe embodiments described herein. Thus, there is a need in the art fornew systems and methods using ubiquitous smart phones which can measurethe refractive properties of an optical system.

BRIEF SUMMARY OF THE INVENTION

Disclosed systems and methods include methods that simulate or replicatean optometrist's cross-cylinder examination that utilizes the inverseShack-Hartmann technique. Disclosed systems and methods include variousimprovements, such as accuracy and usability of the inverseShack-Hartmann technique. The optical input of a disclosed device canoriginate from a smart phone, personal electronic device or otheroptical system, wherein the user will see two parallel lines lookingthrough the other end of the device (e.g. one green and one red)separated by a specific distance d (see FIG. 1). The lines may begenerated from the screen of a smartphone. The high resolution affordedin today's smart phones (e.g. iPhone 6 has a 326 dpi screen resolutionthat corresponds to a pixel spacing of about 78 microns) allows for highresolution measurements of the optical displacement or error ifreferencing an entity such as a focal plane or human retina. After thelight passes through the optical system, at the imaging plane two linesare formed, (see FIGS. 1 and 2) and in a particular embodiment, twolines with “tails”, as seen in FIG. 3, due to the intended coma in thedescribed system. The coma, or comatic aberration, in an optical systemreferring to an aberration inherent to certain optical designs or due toimperfection in the lens or other components that results in off-axispoint sources such as pixels forming a line are appearing distorted,appearing to have a tail (coma) like a comet. Specifically, coma may bedefined as a variation in magnification over the entrance pupil. Inrefractive or diffractive optical systems, especially those imaging awide spectral range, coma can be a function of wavelength, in which caseit is a form of chromatic aberration.

If the imaging system or the eye being tested has a refractive error,the lines will be out of focus and separated, as shown in FIG. 4. Theimaging plane may be the eye retina or the sensor of a CCD camera. Bychanging the distance d (see FIG. 1) between the two lines on the smartphone until the user perceives a zero or near zero distance (see“aligned lines” in FIGS. 3, 4), a refraction error may be assessed.

The distance of the lenslets from the smartphone's screen is D which isequal to the focal length of each lenslet. Thus, after the incidentlight passes through the lenslets, it becomes collimated and focuses onthe focal plane of the lens of the tested lens. If there is a refractiveerror, the red and green lines are separated on the imaging plane asshown in FIG. 4A. If the lines are moved on the screen by changing thedistance d, the position of the two lines on the imaging plane will alsochange. When the two lines are overlapping on the imaging plane therefractive error can be assessed by the amount of change for distance d.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains a least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 depicts a schematic diagram of an overall configuration of adisclosed system with the light source being a smart phone screen, anddepicts the effect of moving the lines by one pixel with size c.

FIG. 2 depicts what a user might see as they operate a disclosed device,using comma-free lines.

FIG. 3 depicts what a user might see as they operate a disclosed device,using non-uniformly broaden fat lines due to intentional comma in theoptical system. The intentional coma helps the user see the pattern andfacilitates the user's alignment of the lines.

FIG. 4A depicts an implementation of the Inverse Shack Hartmanntechnique in an initial position.

FIG. 4B depicts an implementation of the Inverse Shack Hartmanntechnique wherein the pixels have been moved by one pixel

FIG. 5A depicts a display with the pattern used as an input to theoptical system using a rotation of the lines around their center tomeasure different meridians.

FIG. 5B depicts a display with the pattern used as an input to theoptical system using a rotation of the lines around the center of thescreen to measure different meridians.

FIG. 6 depicts simulated crosstalk at the imaging plane in the inverseShack-Hartmann technique using a complex lens as shown in FIG. 8.

FIG. 7 depicts a demagnification stage

FIG. 8 depicts a lens array where an optional lens can be added andwherein the lens array may enable the use of other information,instructions, and patterns

FIG. 9 depicts the usage of an inverse Shack-Hartmann method forvalidating a prescription and for the illustration of results

FIG. 10 depicts exit pupil reduction system in order to make the exitpupil smaller than the entrance pupil of the imaging system.

FIG. 11 depicts an overall disclosed embodiment, based upon the contentof FIGS. 4, 7, 8 and 10.

FIG. 12A depicts graphic representation of the use of the inverseShack-Hartmann technique wherein a disclosed embodiment can simulate across cylinder procedure for accurately estimating the refraction errorand lens properties.

FIG. 12B depicts graphic representation of what the user perceives andthe state on the screen of the phone at the five points illustrated inFIG. 12A.

FIG. 13 depicts a drawing convention for concave and convex lenses asused in the drawings.

FIG. 14 depicts a second disclosed embodiment.

FIG. 15 depicts a disclosed embodiment

FIG. 16 depicts measurement concepts of a disclosed embodiment

FIG. 17 depicts a disclosed embodiment based upon a linear translationmechanism for image modification

FIG. 18 depicts graph of corrective power [D] vs. Translation offsetfrom Nominal [mm]

FIG. 19 depicts an alternative embodiment wherein a first lens isreplaced with a variable focus lens

FIGS. 20A, 20B and 20C depict disclosed embodiments wherein atranslational element moves a display along the optical axis

REFERENCE NUMERALS IN THE DRAWINGS

These and other aspects of the present invention will become apparentupon reading the following detailed description in conjunction with theassociated drawings.

L1 de-magnifying lens

L2 a color lens or second lens

L3 a color lens or another second lens

100 smart phone

110 screen of smart phone

112 display

200 optical system

210 focal plane

220 imaging plane

230 convex lens

240 concave lens

300 eye/imaging system

400 optical axis

500 lenslets

600 complex lens

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The following detailed description is directed to certain specificembodiments of the invention. However, the invention can be embodied inmany different ways as defined and covered by the claims and theirequivalents. In this description, reference is made to the drawingswherein like parts are designated with like numerals throughout.

Unless otherwise noted in this specification or in the claims, all ofthe terms used in the specification and the claims will have themeanings normally ascribed to these terms by workers in the art.

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising” and thelike are to be construed in an inclusive sense as opposed to anexclusive or exhaustive sense; that is to say, in a sense of “including,but not limited to.” Words using the singular or plural number alsoinclude the plural or singular number, respectively. Additionally, thewords “herein,” “above,” “below,” and words of similar import, when usedin this application, shall refer to this application as a whole and notto any particular portions of this application.

Disclosed embodiments may use the inverse Shack-Hartmann method and aprocedure that emulates the cross-cylinder procedure that manyoptometrists use in order to determine refractive errors with highaccuracy.

A method used by an optometrist to accurately measure the refractiveerror of a patient includes: initially the optometrist has a roughestimation of the patient's refractive error and using a cross cylinderor equivalently, a Jackson's cross cylinder, the optometrist canaccurately determine the axis and the amplitude of the astigmatism.Using this method, the optometrist first estimates the prescriptionusing another refractive method such as an autorefractor or retinoscopy.Then the optometrist uses this prescription as a base line and adds apure cylindrical lens with zero spherical equivalent and cylindricalpower 2 C. Thus, the power of the lens on one axis is +C and on theother axis which is perpendicular to the first one is −C. Theoptometrist initially aligns the axis of the estimation of theprescription with the meridian that has 0 power. Then the optometristsflips the lens, changing the polarity of the lens at each meridian orequivalently changes the axis of the cylinder by 90 degrees. If theinitial axis is correct the patient will not notice any difference, theblur would be the same. If the patient notices a difference, the patientchooses the position (axis) that sees the best image. Then, theoptometrist rotates the correcting lens 5 degrees towards the axis thatgave the best quality image. This process is repeated until the patientcannot notice any difference. This is how the axis is determined withhigh accuracy. Then the optometrist fine tunes the power of astigmatism.The optometrist, using the new axis for setting up the lens kit, usesthe same cross-cylinder lens as before but now the axis of astigmatismis parallel with one of the principal meridians of the cross cylinder.The optometrist then flips the cross-cylinder lens and changes the powerof corrective cylinder according to patient's directions (which positionhas the least blur) until the patient cannot notice any difference,perceiving the same blur for both positions of the cross-cylinder.

In a disclosed embodiment, using a simple inverse Shack-Hartmannimplementation to measure the refractive error, the user observes twolines on a screen such as the screen of a smartphone through an opticalsystem as shown in FIG. 1. Then looking through the refractive devicethe user changes the distance between the two lines on the screen untilthe user sees the two lines overlapped. Then the user moves or adjuststhe device to move on to the next meridian, wherein two more lines arepresented to the user. This process emulates the addition of acorrective lens in front of the eye and/or camera until a sharp image isformed.

The optical system, according to regular inverse Shack-Hartmann method,can be a micro-lens array and/or a pinhole array. The distance of theoptical system from the phone screen is defined as D.

FIG. 2 depicts what a user might see as they operate a disclosed device,using a screen pattern of two lines, one red and one green. Theoperation or function of bringing lines together as seen through adisclosed device will be referred to or defined as “alignment”, and atthe end of this process when the lines appeared together and/oroverlapping will be referred to or defined as “aligned”. The minimumdistance that the user can move the lines is limited by the phone'sresolution, namely the pixel distance c, and the distance between thescreen and the optical system D. When the user changes the distance onthe phone it changes the angle of the incident light to the imagingsystem (see FIG. 4). The minimum change in the incident angle to theimaging system θ_(min) can be calculated from the following formula:

$\theta_{\min} = {\tan^{- 1}\frac{c}{D}}$

By knowing the distance d of the two lines on the phone screen, and thedistance D the incident angle can be calculated. From the incident angleθ the power of the refractive error P can be calculated in diopters(m⁻¹). Thus the amount of correction P that is needed can be calculatedusing the following equation:

$P = \frac{2\tan\;\theta}{d^{\prime}}$

where d′ is the distance of the two beams on the lens of the imagingsystem or the size of the exit pupil as shown in FIG. 4B.

Thus the resolution of the refractive error that can be detected in asystem as in FIG. 4B is:

$P_{\min} = {\frac{2c}{{Dd}^{\prime}} = {\frac{2c}{{fd}^{\prime}} = \frac{2c}{f\left( {d - {2{tc}\text{/}f}} \right)}}}$

This formula assumes that the lines are overlapping exactly in thecenter of the imaging plane. As an example, if the pixel distance c is0.78 μm the size of the entrance pupil of the imaging system d′ 1.5 mmand the focal length 10 cm the minimum refractive error that can bedetected is about 1 diopter.

The described measurement takes place one meridian at a time by virtueof using one pair of parallel lines. In order to measure differentmeridians through the camera or human eye, the angle of the parallellines must change with respect to the orientation of the human eye. Atdifferent meridians the space between the lines on the phone screenneeded to reach alignment can be different because the power at eachmeridian changes due to astigmatism. The angle of the lines, andconsequently the meridian that is being tested, can be changed either byrotating the lines around the center of each line or around the centerof the pattern (see FIGS. 5A, 5B). In order to have representativepoints across all the meridians at least one rotation around the centerof the pattern is needed, see FIG. 5B, otherwise the meridian thatcorresponds to the initial meridian plus 90 degrees cannot be measured.When the lines are rotating around the center of the pattern the opticalelements should also follow the rotation of the lines. This can be doneeither by rotating the optical elements to match the rotation of thepattern or by rotating the whole display (phone). One other way is byusing more optical elements (micro-lenses, pinholes etc.). In this casethe pattern is rotated on the phone and uses different lenslets orpinholes to collimate the light. In this case there is crosstalk whichcan confuse the user.

With the technique described herein, disclosed embodiments using theinverse Shack-Hartmann technique, simulates the cross-cylinder procedureused by optometrists. The disclosed embodiments are made possible, inpart, by the several disclosed improvements on the inverseShack-Hartmann method that are disclosed herein. A disclosed opticaldevice may include an array of lenslets and/or pinholes used with alight source as in the Shack-Hartmann technique discussed above. Usingthis disclosed optical device, in conjunction with a smart phone thecross-cylinder procedure described above can be emulated.

In one disclosed embodiment, the screen of the smartphone displayssimultaneously four lines, two pairs of parallel lines, as shown in FIG.9. The two parallel pairs are perpendicular to each other and theseparation of the lines at each pair is always the same. When the userlooks through the optical device the screen of a smartphone he sees twopairs of parallel lines, in total four lines. The distance of the lineswithin a pair that the user perceives depends upon the refractive powerof his eye at the meridian perpendicular to the lines and the distanceof the lines on the phone. If the user has an astigmatic error thedistance of the lines at each pair would be different unless themeridians that are being measured differ by 45 degrees from the axis ofthe astigmatic error (the two meridians that are being measured are thegreen circles in FIG. 12). When the separation of the lines at each pairis different the user rotates the pattern on the screen and hence theangle of the meridians that are being measured is changing, until theuser sees two displaced crosses, FIG. 9 (the lines at each pair areequally spaced). The user adjusts the distance between the lines at eachpair of lines, typically using the controls on the smartphone, to makethe lines come together and overlap, which effectively corresponds tobringing the view into sharp focus.

This procedure is graphically shown in FIG. 12A along with what the userobserves at each step. The blue line represents the power of therefractive error (y-axis) at each meridian (x-axis). At this particularexample a refractive error of 0 spherical −2 cylindrical with axis of 25was used. When the user rotates the pattern on the phone's screen, iteffectively moves horizontally the red circles in FIG. 12A, whichcorrespond to the meridians that are being test. As seen in FIG. 12B onthe screen the lines are rotating around their center but the user seesthe distance of the lines changing. The red squares are always separatedby 90 degrees. When the two meridians under test have the same power(they are at the same angle as the green circles on FIG. 12A) the axiscan be defined. The user knows that the two meridians under measurementhave the same power when he or she sees the lines at each pair equallyspaced, FIG. 12B. It is worth mentioning that during this process thelines at each pair are separated by the same amount. The meridians thatare being measured at this point ±45 degrees from the axis, and hencethe axis is determined.

Then the user changes the power of the spherical equivalent until thelines at each pair are overlapping and the user sees the lines at eachpair are overlapping and if at each pair there is one red and one greenline, the user will see a yellow cross. The change of the sphericalequivalent changes the separation distance at each pair simultaneously.When the lines are overlapping, the spherical equivalent can be inferredby knowing the distance of the lines on the screen. If the user doesn'tsee a cross, this step and the previous step can be iterated until theuser sees a yellow cross (where the red and green lines overlap). At theend of this measurement the axis of astigmatism and the sphericalequivalent has been determined.

The next step is to determine the power at the axis of the astigmaticerror, namely the cylinder. At the beginning of this stage the app orthe user rotates the pattern on the phone by 45 degrees compared therotation at the previous step so one of the pairs is parallel to theaxis of astigmatism and the second pair to be perpendicular to the axisof astigmatism. Now the user changes the power of the cylinder bychanging the separation of the lines at each pair until a yellow crossis formed as before, or equivalently the gray circles coincides with theblack circles in FIG. 12A. From this last measurement, the power of thecylinder is determined.

In sum, the following steps are sometimes used to measure the refractiveerror of the user using this disclosed:

1. The user looks through the device viewing the smartphone's screenseeing the four lines on the phone screen, FIG. 9

2. Rotate the cross pattern on the device until the distance between thetwo lines at each pair (red and green) is the same;

3. Change the spherical equivalent power by changing the distancebetween the lines until the user sees a yellow cross or as close aspossible;

4. Iterate steps 2 and 3 until the user sees a yellow cross in themiddle of the field of view;

5. Rotate the pattern by 45 degrees in order to measure the power of themeridians that have the minimum and maximum power;

6. Change the cylindrical power, the amplitude of the sinusoidal in FIG.12A until the user sees a yellow cross.

An advantage of this disclosed method is that the measurement is takingplace at two meridians, 90 degrees apart, simultaneously. Thus the eyeis at the same state when the measurement is taking place at bothmeridians. Hence, a more accurate measurement of the refractive errorsis expected or at least a measurement that will yield better visualacuity results, since the estimation of the cylinder and the axis willhave less noise. This is true because this method avoids errors inastigmatism due to fluctuation of the accommodation (e.g. dark focusvariation, instrument myopia, etc.) since the measurements needed toestimate the amplitude and the axis of the astigmatism take place at thesame time.

To realize this cross-cylinder method, the inverse Shack-Hartmann deviceas shown in FIGS. 4A and 4B and described above needs some improvementsas compared to the current state of the art. First, the device should becapable of handling multiple meridians at the same time. Thus at leasttwo pairs of lenslets are needed (in total four lenslets). In this caselight that was supposed to pass through a specific lenslet insteadpasses through another lenslet and confuses the user by creatingmultiple images. FIG. 6 shows this effect, which from now on we refer toas crosstalk. One way to reduce the crosstalk is to increase thedistance between the two lenslets, FIG. 8, or include a baffle betweenthe two lenslets. This way the resolution is increased (larger d′), butthe exit pupil becomes larger too. In the case of the human eye, thisreduces the field of view making the alignment very sensitive, as thehuman pupil is typically 3 to 6 mm in our conditions (1.5 mm in a verybright environment and 8 mm in an environment with very little light).Also, the resolution of the device can be improved by 2 times byallowing the overlapping to be around the center and not exactly at thecenter by moving one row of pixels at the time. This resembles more thereality since the lines can overlap in the center of the imaging planeonly when the resolution of the device match exactly the refractiveerror of the user. Finally, we intentionally induced comma in our systemto aid the user with the decision making. In this case the two lines arealigned when they slightly touch at the imaging plane—the user cannotsee a black line between the green and red line and/or the two lines areslightly touch and a slight yellow line is formed (red and green linesare overlapped) FIG. 3.

Thus, for an ideal device high resolution is needed with a small exitpupil/large field of view, low crosstalk and an easy way for the user tomake a decision when the lines are aligned, when using a subjective testmethod.

Definition of the Subsystems

To resolve the aforementioned issues, the following subsystems may beused:

A demagnification subsystem which comprises a single concave lens. Thisstage improves the resolution substantially, FIG. 7;

four lenses, 2 mm thick, 6 mm apart (center from center) to decreasecrosstalk (less light that intended for one lens passes through thesecond lens and the image that is created is relatively far away) anddefocus issues (small aperture 2 mm thick). An extra shutter in form ofslits can be used in the lenses in order to further improve theusability in optical systems with higher refractive errors. Thesedimensions are provided as an example, however the invention is notlimited to these parameters;

Magnification stage to reduce the exit pupil and improve the field ofview, to further reduce crosstalk and induce comma to improve userexperience.

Finally a shutter in form of a slit can be used just before the lens ofthe optical system under test in order to increase the depth of field.This way the blur observed by people with high refractive errors isminimized due to the small aperture in one direction and at the sametime the light is attenuated much less compared to a pinhole.

FIG. 7 shows the demagnification concept, which increases the effectiveresolution of the mobile screen. To improve the resolution, a subsystemis introduced that comprised of one concave lens. The concave lenscreates a new virtual image that is smaller than the original image. Ifthe concave lens with focal length f from the image is L then a change hin the distance from the optical axis converts into a distance h′, andhence the effective pixel density is increased. The demagnificationfactor DM=h/h′, the amount the linear pixel density is increased, isgiven by:

${DM} = {\frac{h}{h^{\prime}} = {1 + \frac{L}{f}}}$

Thus by either increasing the distance from the screen or by decreasingthe focal length of the lens, the demagnification factor can beincreased. This can increase the effective resolution and it can haveother applications not limited to this device, e.g. it can be used toincrease the resolution for VR headsets. The virtual image is formed indistance L/DM behind the concave lens (towards the screen). This has aneffect of increasing the linear pixel density by a factor of DM, orequivalently to decrease the minimum pixel distance by a factor of DM.

FIG. 8 shows a lens array where an optional lens can be added thatallows transmission of other information, instructions, and patterns. Inthis setup four lenslets are used to avoid rotation/crosstalk/defocus(four lenslets at a relatively far distance) with a fifth optionallenslet in the center of the array for allowing other optical images tobe presented to the user. Other optical images can be used forcontrolling accommodation, or sending the user visual information and/orinstructions. The four lenslets may be 2×4 mm in order to act as a smallshutter and reduce the crosstalk. Light intended to go through one lensis poorly coupled to the lenses that are oriented perpendicular to theinitial lens. The lenslets are used in pairs as described in thebeginning of this document (lenses 1, 2 and 3, 4, FIG. 8), namely tocreate two collimated beams. The crosstalk is reduced because light thatwas directed through one 1 and 2 is poorly coupled to lenses 3 and 4because of their shapes and vice versa. The lenslets are 6 mm apart toreduce crosstalk.

FIG. 9 shows the usage of lenses and the checking of results. To checkthe validity of a test result, namely if the system estimated correctlythe refractive properties of the user's eyes or the device under testall four lenslets can be used simultaneously, as in the cross-cylindermethod. The distance of the lines on the screen is set based on theresult and the meridian under measurement. If the result is correct, theuser will see a cross. For example, if the result shows a cylinder at 8degrees and we want to check the cylinder one pair of lenses is set tomeasure at 8 degrees and the second pair at θ+90 modulo 180 degrees.

If measurement of the spherical equivalent is desired, a measurement atθ+45 modulo 180 degrees and at θ−45 modulo 180 degrees can be taken. Atthose two meridians if the estimation of the refractive error is correctthe power of lens under test should be equal to spherical equivalent. Ifthe user sees 4 lines, then the test result is incorrect (in FIG. 9indicates wrong result). If the user sees a cross the result is valid(indicated in FIG. 9 as correct result). This way, experimentalvalidation of the result can be produced by simultaneously measuring twomeridians.

Using four lenslets relatively far away from each other with an optional5^(th) lens, crosstalk is reduced as well as any mechanical rotation isavoided, while any meridian lends itself to measurement. At the sametime, the fifth lens can be used to provide the necessary stimuli inorder to control the user's accommodation and project to him otheruseful information. The downside is that the exit pupil is pretty largeand the field of view small. This issue will be addressed by the nextsubsystem.

FIG. 10 shows exit pupil reduction, crosstalk reduction, and comainducer optical system. The induced coma helps to improve usability.This subsystem has three objectives. The main objective is to reduce theexit pupil and hence to increase the field of view. Second, thecrosstalk that the user perceives is further reduced because thecrosstalk image is outside of user's field of view. Finally, this setupinduces coma, making the lines easier to see and align (the fat lineeffect shown in FIG. 2).

This setup or disclosed configuration comprises a convex lens with focallength f₁ and a concave lens with focal length f₂. The two lenses sharethe same focal plane. The input in this system is the output of thelenslets array thus it is two collimated beams. In order to make it easyto analyze this subsystem, it shall be assumed that the two beams areparallel to the optical axis. The convex lens focuses the two parallelbeams. This brings the two beams closer, and hence reduce the exitpupil. Before they reach the focus the concave lens intervenes and thetwo beams become parallel again, but now are much closer. The amount ofthe reduction of the exit pupil (d/d′) equals to the ratio of the focallengths of the two lenses (f₁/f₂). This has as an effect of decreasingcrosstalk (the concave lens acts as a beam expander, and increases theangular separation between the main beams and the beams due tocrosstalk). A second positive side-effect of this system is the comainduction. Because the edge of a spherical lens is used and isconverted, an induced coma to the collimated beams is created. Thisresults in a sharp line with a faded tail as shown in FIG. 3. This makesthe alignment process more objective and the lines easier to find.Ideally, the user will place the two lines very close in order to see aslight yellow line and no gap (see FIG. 3). The downside of this systemis that the resolution is significantly reduced. Two phenomena result inthe reduction of the resolution: (1) the distance of the parallel beamis reduced which directly affects the resolution; and (2) for the samepixel movement there is a larger change in the incident angle to the eyewhich results in lower resolution.

FIG. 11 shows an overall disclosed system, including a description ofthe overall system and the optical parts. The previous subsystems, FIGS.7, 8, 10 are realized into one complete optical system which maycomprise:

A concave lens to reduce the minimum refractive error;

A lens array that collimates the light from the virtual image that iscreated using the concave lens, together with the convex lens of thethird subsystem. This custom/complex optical element increases thetransmission by approximately 8.6% and reduces the manufacturing costsignificantly compared of using separate optical elements; and

a second concave lens to prepare the light for the imaging system.

Thus the light from the phone display screen first passes through thefirst concave lens in order to increase the effective resolution. Thenthrough a convex lenslet that is off-axis to the whole system tocollimate the light parallel then to another convex lens, followed by aconcave lens to reduce the exit pupil and reduce crosstalk. In order tohave a calibrated measurement, the device should have an initialcalibration. This can be done using a camera focused at infinity(emulates an emmetropic eye). Then an artificially induced error iscreated by adding a prescription lens from a trial lens-kit in front ofthe camera. Afterwards, the lines are moved until they touch and theamount of displacement is logged with the induced refractive error. Thisway, the refractive error can be determined by knowing the displacement.

In another embodiment of this invention the complex lens and thedemagnification stage can be replaced with a pair of colored lens and aslit for each lens mounted on a rotating mount, as shown in FIG. 14. Thecolored lens act as a filter to eliminate crosstalk. One lens can becolored red and the second one green. Thus, the light emitted from thegreen line cannot pass through the red colored lens and vice-versa.After each lens there is a slit that act as a shutter and increase thedepth of field. Again, the usage of the slits doesn't reduce much thetransmitted intensity. In this embodiment, there is no need of themagnification stage, since the exit pupil is determined solely by thedistance between the two slits, and the crosstalk is eliminated by usingcolored lenses. In order to measure meridians at different angles thelens along with the slits are rotating using a rotating mount andfollows the rotation on the screen. The rotation can happen eithermanually by the user or by using an electric motor. When the userproceed to the next meridian the application can automatically rotatethe rotating mount.

Mechanical Tolerance Analysis.

If the whole system is translated parallel to the screen in a firstorder approximation, the error in the assessment of the refractive errorwould be minimal. The only effect it would have is that the user won'tsee the lines symmetrically around the center of its field of view andthe intensity would be reduced. Next, every subsystem will be analyzedseparately, focusing on the lateral displacement. The tilt tolerance canbe easily calculated by converting the lateral tolerance into an angle(shown in the end of this section).

a. Demagnification

The demagnification is given by:

${DM} = {\frac{h}{h\;\prime} = {1 + \frac{L}{f}}}$

and the position of the virtual image and the size is respectively

${L^{\prime} = \frac{fL}{L + f}},{h^{\prime} = \frac{fh}{L + f}}$

so a change of ΔL will induce a change in demagnification of

${\Delta\;{DM}} = \frac{\Delta\; L}{f}$

in the position of the virtual image of

${\Delta\; L^{\prime}} = {{\frac{f^{2}}{\left( {L + f} \right)^{2}}\Delta\; L} = \frac{\Delta\; L}{{DM}^{2}}}$

and the size of the virtual image:

${\Delta\; h^{\prime}} = {{{- \frac{fh}{\left( {L + f} \right)^{2}}}\Delta\; L} = {{- \frac{h}{f}}\frac{\Delta\; L}{{DM}^{2}}}}$

The change in the size of the virtual image will directly induce a shiftin the calibration, the change in the demagnification will directlyaffect the resolution of the system and the change in the positionaffects the performance of the following subsystems. The resolution islimited by c (pixel spacing) over DM so:

${\Delta\;{Resratio}} = {{{- \frac{1}{{DM}^{2}}}\Delta\;{DM}} = {{- \frac{1}{f}}\frac{\Delta\; L}{{DM}^{2}}}}$

So if the demagnification factor is 3, the device is 9 times lesssensitive. Hence in terms of tolerance it is beneficial to have highdemagnification. It is even better to have long focal length. Therefore,it is preferable to achieve large magnification using longer length.

b. Parallel Beam Creation

If the optical source is not exactly on the focal point of the lensletthe beam after the lenslet will be either diverging or converging. Thusit will bias, shift our measurements. Thus our measurement of the powerwill be shifted by

${\Delta\; P} = {{- \frac{1}{D^{2}}}\Delta\; D}$

From this equation the change in the power due to the demagnificationcan be calculated as:

${\Delta\; P_{demag}} = {{{- \frac{1}{\left( {f_{l} + L^{\prime}} \right)^{2}}}{\Delta\left( {f_{l} + L^{\prime}} \right)}} = {{- \frac{1}{\left( {f_{l} + L^{\prime}} \right)^{2}}}\frac{\Delta\; L_{d}}{{DM}^{2}}}}$

This change adds up with the bias due to change in demagnification andreduces the total effect.

c. Magnification Stage

This stage doesn't depend on the previous stage. It solely reduces thedistance between two beams. If the distance between the two lenses isnot correct, it will induce a bias in the refraction measurement. Againwith a first order approximation is

${\Delta\; P} = {\frac{1}{L^{2}}\Delta\; L}$

The dominant factor is the lateral change of the demagnification stageand mainly the change in the distance of the two lines (2h′). Thischange in height induces a bias on the measured power. For lowresolution the change in resolution due to the change in thedemagnification is important especially for people with high refractiveerror. As an example, for a design with a demagnification factor equalto 3, and the distance between lines equal to 18 mm, and the distance ofthe concave lens from the screen equal to 30 mm.

Tilt can be converted into lateral displacement (at least in a firstorder approximation). Focusing only on the demagnification stage, whichis the stage with the tightest tolerances, if the lens is tilted aroundthe center, one side of lens comes closer to the screen and the otherfurther away. Thus the net effect is zero. If the lens is tilted on thecorner, only one side moves and the change in length is ΔL≈2hΔθ. Theangle converts into a Power bias as follows:ΔP=−14.4Δθ(radians)=−0.25Δθ(degrees)

Further Embodiments Include

Some current apparatuses and methods include lens-based refractometersthat attach to a smartphone and work with a smart phone app that allowsfor accurate measurement of the optical system refractive error. In thecase of the measured optical system being the human eye, an example ofsuch a device is the Personal Vision Tracker (PVT) by EyeQue Corp(patent publication US20170215724A1 incorporated herein in its entiretyas reference).

The PVT works by projecting an image of a defined geometrical patternonto the user's retina, allowing the user to control an aspect of theproperties of the image to achieve a well-defined goal, and thenmeasuring a parameter of the image to deduce the required correction ofthe user optical system (e.g. their eye). As an example, the image couldbe on a screen of a smartphone to which an optical device is attached.Furthermore, an example of the image could be a set of parallel lines ofdifferent color (e.g. red and green). As the image is transmittedthrough the optical device the user adjusts the perceived distancebetween the lines on the screen to get them to a final position such asthey appear in a well-defined relation, for example overlapping. Therelation between the distance between the lines and the perceivedoverlap corresponds to the user's refractive error. An example of thisimplementation is shown in FIG. 15.

Referring to FIG. 15, this method and apparatus are limited in themeasurement accuracy by the resolution of the phone. In today'ssmartphones the pixel density (resolution measured in pixels per inch,ppi) is around 326. There are phones that have higher resolutions (mostcommon around 570 ppi) and phones with lower resolutions (down to below250 ppi). The 326 ppi phones allow for accuracy in the order of 0.25 Dwithin the scale of −10 D and +8 D. This accuracy level is adequate inmost cases but might be a bit limiting (especially for lower resolutionphones). Furthermore, this method requires an active display to controlthe distance between the lines.

As an alternative to this apparatus and method, the current inventionproposes the following implementation of the refraction measurement. Adisplay showing a geometrical image (for example to parallel lines, onegreen and one red) is presented to the user through an optical system(for example the system presented in FIG. 15). The user then controlsthe geometrical representation of the image through the measured opticalsystem. In an embodiment of the invention, the control is done bymodifying the distance of the display from the first lens. In anotherembodiment of the invention the control is done by modifying the focallength of the lens at the end of the device optical system, for exampleby using a variable focus lens, a zoom lens, or a liquid lens. Themodification of the image by the user through the measured opticalsystem is done to achieve a specific geometrical goal, for exampleoverlapping of the lines. The system parameter (whether it is thedistance offset, or the adjusted focal length of the lens is thenrecorded and correlated with the required optical correction of themeasured system. An example of a measured system could be the user'seye. The correlation could be done for example by calibration, fittingto a curve/function, analytical or numeric calculation, by artificialintelligence, e.g. neural networks.

Referring to FIG. 16, an explanation of a disclosed measurementprinciple is presented. At a nominal location of the display from thefirst lens of the device, the presented lines on the display appear tooverlap on the focal plane of the measured optical system (e.g. theretina of the eye). As the display is translated away from the measuredoptical system, the lines appear to be getting farther away from eachother in one direction, as the focal point (where the lines intersect)moves farther from the device. As the display is translated towards thefirst lens, the lines separate to the other direction and the focalpoint is shifted towards the device.

Referring to FIG. 17, an embodiment of the proposed invention based onthe linear translation mechanism for the image modification ispresented.

An optical refractor may comprise a demagnifier lens, L1, and twocolored lenses, L2, green, and L3, Red. Adjacent to L2 and L3 are slitsthat allow passage of red and green light respectively. The resolutionof the device can be determined by following the chief rays of the twolines at incremental distances of the screen from the first lens.

Referring to 18, a power-distance relation in a disclosed embodiment isshown. It should be noted that the dependency is not linear as to beexpected. The slope of the curve determines the resolution. The expectedaverage resolution in the presented case is approximately 2.5 D per mm(100 μm corresponds to about 0.25 D). The resolution of the device maybe increased by changing the nominal distance between the lines or byincreasing the focal length of the first lens as the angular sentence Ψof the two lines decrease. The resolution of the device is proportionalto 1/tan(Ψ).

FIG. 19 presents an alternative embodiment of the invention where thefirst lens is replaced with a variable focus lens. In this embodiment,the focal length of the first lens is changed to achieve overlap betweenthe lines on the display in the focal plane of the measured opticalsystem (e.g. the retina for the human eye). FIG. 19 also shows the raytracing of the nominal lens power as well as two other possible powersone, higher power (shorter absolute focal length, in the example case,more positive power) of the first lens will correspond to the focalpoint of the two lines intersecting to be farther from the device, whilea lower power (longer absolute focal length, and in the example case,more negative power) corresponds to the lines intersecting closer to thedevice.

As the modification mechanism is independent of the actual distancebetween the lines the display could be of a multitude of optionsincluding for example: a screen (including a smartphone screen), an LEDstrip (including one where the lines are made of diffusers ad colorfilters), a semitransparent plaque with backlight, a light boxilluminating a mask transmitting the desired pattern.

To get a measure of the astigmatic aspect of the measured optical system(e.g. the eye), the device can be rotated through different meridiansand the resultant data of required corrective optical power can be usedto compute the refractive error of the measured optical system in Focus(Sphere) and Astigmatism (Cylinder, and Axis).

Referring to FIGS. 20A, 20B and 20C, alternatively, the display, colorlenses and slits could be rotated in correspondence, instead of theentire device.

In an embodiment of the invention, a translational element moves adisplay along the optical axis, and a single rotational element allowsthe slits and color lenses on the eye piece and the display to rotate intandem through different meridians (FIG. 20A). In another proposedembodiment of the invention the rotation is achieved by implementing tworotational elements, one on the display and another for the slits andcolor lenses (FIG. 20B). In this embodiment special care needs to betaken for the synchronization between the rotational elements. In yetanother implementation of the invention, the rotation of the display isdone by digital means, with the display being an electronic screen. Inthis case the rotation of the slits and color lenses is done by arotational element (FIG. 20C).

Both linear translation elements and rotational elements could be ofvarious manifestations including for example, fully manual control,completely automatic or electronic control and any combination thereof.The proposed embodiments could be implemented in either a monocular orbinocular form. In an embodiment of the invention, the device wouldconnect to a smart phone or other Bluetooth enabled computational deviceto transmit data to perform calculations and analysis on thecomputational device or enabling transmission of the data to a cloud toperform the calculations and analysis there. The connection may also beused for control of the different aspects of the device for example therotation and translation of the corresponding elements.

The above detailed description of embodiments of the invention is notintended to be exhaustive or to limit the invention to the precise formdisclosed above. While specific embodiments of, and examples for, theinvention are described above for illustrative purposes, variousequivalent modifications are possible within the scope of the invention,as those skilled in the relevant art will recognize. For example, whilesteps are presented in a given order, alternative embodiments mayperform routines having steps in a different order. The teachings of theinvention provided herein can be applied to other systems, not only thesystems described herein. The various embodiments described herein canbe combined to provide further embodiments. These and other changes canbe made to the invention in light of the detailed description.

All the above references and U.S. patents and applications areincorporated herein by reference. Aspects of the invention can bemodified, if necessary, to employ the systems, functions and concepts ofthe various patents and applications described above to provide yetfurther embodiments of the invention.

These and other changes can be made to the invention in light of theabove detailed description. In general, the terms used in the followingclaims, should not be construed to limit the invention to the specificembodiments disclosed in the specification, unless the above detaileddescription explicitly defines such terms. Accordingly, the actual scopeof the invention encompasses the disclosed embodiments and allequivalent ways of practicing or implementing the invention under theclaims.

While certain aspects of the invention are presented below in certainclaim forms, the inventors contemplate the various aspects of theinvention in any number of claim forms.

The disclosed embodiments may include the following items:

1. A method to measure refraction errors in an optical system (300),using a first lens (200), a second lens and a display (112) the methodcomprising the steps of:

disposing the second lens proximal to the optical system;

disposing the first lens within sight lines of the second lens;

disposing the display within sight lines of the first lens;

changing the distance of the display from the first lens until anindicia upon the display is aligned as observed by the optical system;

using the changed distance of the display to derive spherical error ofthe optical system.

2. The method of item 1 wherein the first lens comprises ademagnification lens.

3. The method of item 2 wherein the second lens comprises a firstcolored lens and a second colored lens.

4. The method of item 3 wherein the second lens defines two slits.

5. The method of item 4 wherein the indicia transmitted from the secondlens to the optical system comprises first color and a second color.

6. The method of item 1 wherein the indicia upon the display comprises afirst symbol and a second symbol.

7. The method of item 6, wherein the first and second symbols arerespectively, vertical and horizontal colored lines.

8. The method of item 7, wherein the colored lines are red and green.

9. The method of item 1 wherein the display comprises one of thefollowing selected from the group compressing (a screen ((including asmartphone screen)), an LED strip ((including one where the lines aremade of diffusers and color filters)), a semitransparent plaque withbacklight, a light box illuminating a mask transmitting the indicia.

10. The method of item 1 further including the step of rotating thesecond lens along an optical axis through different meridians andmeasuring the distance of movement of the second lens at each meridianin response to a changed projection upon the screen and using themeasured distances of the second lens to derive further errors ofrefraction of the optical system.

11. The method of item 1 further including the step of rotating thedisplay in synchronization to a rotation of the second lens along anoptical axis through different meridians and measuring the distance ofmovement of the second lens at each meridian and using the measureddistances of the second lens to derive further errors of refraction ofthe optical system.

12. A method to measure refraction errors in an optical system (300),using a first lens, a second lens and a display (112) the methodcomprising the steps of:

disposing the second lens proximal to the optical system;

disposing the first lens within sight lines of the second lens; whereinthe first lens is a variable focus lens;

disposing the display within sight lines of the first lens;

changing the focal length of the first lens until an indicia upon thedisplay is aligned as observed by the optical system;

using the changed focal length of the first lens to derive sphericalerror of the optical system.

13. A system to measure refraction errors in an optical system (300),comprising a first lens, a second lens and a display the systemcomprising:

the second lens disposed in a position proximal to the optical system;

the first lens disposed within sight lines of the second lens;

the display disposed within sight lines of the first lens;

the display having an adjustable linkage from the first lens with theadjustable linkage having means to adjust in length until an indiciaupon the display is aligned as observed by the optical system;

the changed distance of the display functioning as a variable to derivespherical error of the optical system.

14. A system to measure refraction errors in an optical system (300),comprising a first lens, a second lens and a display (112) the systemcomprising:

the second lens disposed proximal to the optical system;

the first lens disposed within sight lines of the second lens; whereinthe first lens is a variable focus lens;

the display disposed within sight lines of the first lens;

means to measure change in the focal length of the first lens used toaligned indicia upon the display as observed by the optical system;

the changed distance of the focal length of the first lens used as avariable to derive spherical error of the optical system.

What is claimed is:
 1. A method to measure refraction errors in anoptical system, using a first lens, a second lens and a display themethod comprising the steps of: a. disposing the second lens proximal tothe optical system; b. disposing the first lens within sight lines ofthe second lens; c. disposing the display within sight lines of thefirst lens; d. changing the distance of the display from the first lensuntil an indicia upon the display is aligned as observed by the opticalsystem; e. using the changed distance of the display to derive sphericalerror of the optical system; and f. the second lens comprises a firstcolored lens and a second colored lens.
 2. The method of claim 1 whereinthe first lens comprises a demagnification lens.
 3. The method of claim1 wherein the first colored lens defines two slits and and wherein thesecond colored lens defines two slits.
 4. The method of claim 1 whereinthe indicia transmitted from the second lens to the optical systemcomprises a first color and a second color.
 5. The method of claim 1wherein the indicia upon the display comprises a first symbol and asecond symbol.
 6. The method of claim 5, wherein the first and secondsymbols are respectively, vertical and horizontal colored lines.
 7. Themethod of claim 6, wherein the colored lines are red and green.
 8. Themethod of claim 1 wherein the display comprises one of the followingselected from the group compressing a screen, an LED strip, asemitransparent plaque with backlight, a light box illuminating a masktransmitting the indicia.
 9. The method of claim 1 further including thestep of rotating the second lens along an optical axis through differentmeridians and measuring the distance of movement of the second lens ateach meridian in response to a changed projection upon the screen andusing the measured distances of the second lens to derive further errorsof refraction of the optical system.
 10. The method of claim 1 furtherincluding the step of rotating the display in synchronization to arotation of the second lens along an optical axis through differentmeridians and measuring the distance of movement of the second lens ateach meridian and using the measured distances of the second lens toderive further errors of refraction of the optical system.
 11. A methodto measure refraction errors in an optical system, using a first lens, asecond lens and a display the method comprising the steps of: a.disposing the second lens proximal to the optical system; b. disposingthe first lens within sight lines of the second lens; wherein the firstlens is a variable focus lens; c. disposing the display within sightlines of the first lens; d. changing the focal length of the first lensuntil an indicia upon the display is aligned as observed by the opticalsystem; e. using the changed focal length of the first lens to derivespherical error of the optical system.
 12. A system to measurerefraction errors in an optical system, comprising a first lens, asecond lens and a display the system comprising: a. the second lensdisposed in a position proximal to the optical system; b. the first lensdisposed within sight lines of the second lens; c. the display disposedwithin sight lines of the first lens; d. the display having anadjustable linkage from the first lens with the adjustable linkagehaving means to adjust in length until an indicia upon the display isaligned as observed by the optical system; e. the changed distance ofthe display functioning as a variable to derive spherical error of theoptical system.
 13. A system to measure refraction errors in an opticalsystem, comprising a first lens, a second lens and a display the systemcomprising: a. the second lens disposed proximal to the optical system;b. the first lens disposed within sight lines of the second lens;wherein the first lens is a variable focus lens; c. the display disposedwithin sight lines of the first lens; d. means to measure change in thefocal length of the first lens used to aligned indicia upon the displayas observed by the optical system; e. the changed distance of the focallength of the first lens used as a variable to derive spherical error ofthe optical system.